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bout 4.45 billion years ago, a young planet
Earth - a mere 50 million years old at the
time - experienced the largest impact event of
its history. Another planetary body with roughly
the mass of Mars had formed nearby with an
orbit that had, by chance, placed it on a collision
- - - - - - - - - - - - - course with Earth. When young Earth and this
By Robin Canup, Ph.D.
rogue body collided, the energy involved was
100 million times larger than the much later
event believed to have wiped out the dinosaurs.
The early giant collision destroyed the rogue
body, likely vaporized the upper layers of
Earth's mantle, and ejected large amounts of
debris into Earth orbit. From this debris our
moon coalesced, pOSSibly on a time scale as short
as one to 100 years.
This giant impact scenario of lunar formation represents an important piece of our overall
understanding of the origin of the terrestrial, or
Earth-like, planets in the solar system, which
include Mercury, Venus, Earth, and Mars. In
turn, understanding the origins of planets in our
solar system is the key to determining the likelihood of habitable planets in extrasolar systems.
A research group in the Space Studies
Department of the Southwest Research Institute
(SwRI) Instrumentation and Space Research
Division studies the origins of planetary bodies
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using both theoretical and computational
methods. The group includes the author,
Institute Scientist Dr. William Ward, Space
Studies Department Director Dr. Alan Stern,
Principal Scientist Dr. Harold Levison, Senior
Research Scientist Dr. Luke Dones, and
Postdoctoral Researcher Dr. Daniel Durda.
Recently, research and computational facilities
funded by NASA, the National Science
Foundation, and SwRI's internal research
program have been directed toward developing
improved models of an impact-triggered
formation of the moon and examining the
related implications for the likelihood of similar
planet-moon systems around other stars.
Evolving theories of lunar origin
Compared to other moons and their
planets, the Earth's moon is unusual in several
respects. It is large relative to the Earth, with a
density that is abnormally low compared to the
terrestrial planets, indicating that it lacks highdensity iron. Recent findings even suggest that
the moon's core constitutes only 2-4 percent of
its total mass, compared to a terrestrial core
with about 30 percent of the Earth's mass. The
Earth-moon system also has an abnormally
large angular momentum per unit of
mass, contained in both the Earth's spin
and the moon's orbit, compared to other
planet-satellite systems.
Prior to the 1970s, there were three
main theories regarding the origin of the
moon. The first involved a fission event,
in which the moon broke off from a
rapidly spinning Earth. A co-formation
theory proposed that the Earth and moon
formed contemporaneously as a gravitationally bound pair. The third theory suggested that the moon formed as an
independent planetary body that was
later "captured" by the Earth during a
close pass. Each theory had deficiencies.
For example, it was difficult in both the
capture and co-formation models to
account for the lack of a large lunar iron
core, because both predicted that the
moon formed from the same mix of materials as the terrestrial planets, which typically contain a more substantial
abundance of iron.
One of the main scientific objectives
of the Apollo space program was to differentiate between these theories to
resolve the question of lunar origin.
However, the analysis of lunar samples
raised new questions and challenges.
Relative to terrestrial samples, lunar
material was discovered to be deficient
in volatile materials - those that vaporize and escape easily when
heated - implying that the
moon had undergone some
intense thermal processing
compared to that experienced
by the Earth. In addition, the
abundance of siderophile, or
"iron-liking," elements in
lunar rocks suggested that the
moon was derived from material that had once been part of
the mantle of a larger body
with a sizeable iron core.
In 1976 and 1977, two
groups* proposed a new theory for lunar origin: the giant
impact scenario. The idea was
that an off-center impact of a
roughly Mars-sized body with
early Earth could provide
Earth with its high initial spin,
needed to explain the current
system's angular momentum,
and eject enough debris into
orbit to form the moon. If the ejected
material came primarily from the
mantles of the Earth and the impactor,
the lack of a sizeable lunar core was
easily understood, and the energy of the
impact could account for the extra heating of lunar material required by lunar
volatile depletions.
For nearly a decade, the giant impact
theory was heavily critiqued. The idea
that the moon was the result of a particular large impact event was considered too
arbitrary, and did not fit in well with the
existing view of a quiescent planet formation process. In 1984, a conference
devoted to lunar origin prompted critical
comparison of the existing theories. The
giant impact theory emerged from this
conference with nearly consensus support, enhanced by new models of planet
formation that suggested large impacts
might indeed be common events in the
end stages of terrestrial planet formation.
Such models demonstrated that the relatively quiescent stage of planetary
growth continued only until young planets grew to sizes ranging from lunar to
Mars-sized, and that the final stages of
growth were characterized by collisions
among tens to hundreds of these large,
planet-sized bodies. In the course of the
many impacts apparently required to
yield the final four terrestrial planets, it
did not then seem so unreasonable that
one of the impacts would be of the type
required to yield the moon.
Modeling the moon-forming impact
Clearly the impact of a Mars-sized
body with Earth cannot be reproduced
experimentally. For this scale of an event,
researchers must rely on computer simulations that can be compared with experimental results at small sizes and then
extrapolated to the larger scales of interest
with relative confidence. For modeling
the moon-forming collision, impact energies of interest are high enough to cause
excessive heating and phase changes, and
a hydrodynamic treatment with an appropriate equation of state is required. The
self-gravity of the material involved in the
impact must also be tracked explicitly
because of the large total mass and the
deformation of the bodies that occurs
during an impact. Finally, a simulation
must be able to both achieve high spatial
resolution at the point of contact between
the two planets when they initially
collide, and track the dynamiCS and thermal properties of material ejected into
distant orbits.
The method typically used to simulate planet-scale collisions is the
smoothed-particle hydrodynamics (SPH)
method. Using this technique, the mater. ial in a simulation is represented by a
finite number (typically 10,000 or so)
Dr. Robin Canup, a senior research scientist in the Boulder, Colorado, office of the
SwRllnstrumentation and Space Research Division, specializes in models relating to
the origin of the Earth-moon system, the formation of terrestrial planets, and the origin
of planetary ring and satellite systems. Contact Canup at (303) 546-6856 or
robin @boulder.swri.edu.
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These models show lunar accretion
from a swarm of debris produced by
a single impact event. Midway
through the accretion process, a
system of inner rings and outer
moonlets, similar to those of the
outer planets, form around the
Earth. Such systems are dynamically unstable, however, because
the moon's gravity tosses the inner
small debris onto the Earth leaving
a single large moon. What about the
two-moon model shown at right?
Recent work by the author, Or.
Harold Levison, and Or. Glen
Stewart of the University of
Colorado following the long-term
evolution of these two-moon systems has demonstrated that they
are always unstable: The moons
either collide or the inner moon
crashes into the Earth in both cases leaving the
planet with a single moon.
Single Impact Models
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of discrete, overlapping particles that
approximate a continuous distribution of
matter. Each particle has a mass, internal
energy, and three-dimensional spatial
density probability distribution. At a
given point in space, the local density of
material is then calculated by summing
over the contributions from the nearby
particles. The evolution of the particles is
tracked individually, so that the computational resolution effectively follows the
material wherever it goes. At each timestep in the simulation, forces such as pressure and gravity are calculated, and the
particles are accelerated accordingly. The
equation of state relates pressure to internal energy and denSity, taking into
account such factors as latent heat of
phase changes.
An SPH simulation of a potential
moon-forming impact requires months
of computational time on a single workstation. However, faster simulation
speeds and increased resolution with
greater numbers of particles are possible
through the use of parallel computing.
SwRI scientists are currently collaborating with Dr. Erik Asphaug, of the
University of California at Santa Cruz,
in the development of parallelized
SPH methods.
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calculates the gravitational force on each
particle caused by every other particle in
the simulation at each time-step. When
orbiting particles collide with low enough
impact energies, the result is a gravitationally bound aggregate. Such aggregates continue to grow in size as they
collide, forming larger and larger bodies
in a process called accretion.
Based on this model, the first question to be addressed was, why would a
swarm of debris orbiting close to the
Earth yield a single large moon when we
find systems of multiple moons and rings
around the gas giant planets? For a prelunar debris swarm, most of the accretion
simulations predict the formation of one
large moon orbiting at a characteristic
distance of about 3-5 Earth radii
(12,500-20,000 miles) from the center of
the Earth. The moon's current distance is
about 60 Earth radii (240,000 miles).
However, we know that the tidal interaction between the Earth and moon that
gives rise to our twice-daily oceanic tides
has also caused the lunar orbit to expand.
Thus the moon was much closer to the
earth when it formed, appearing more
than 10 times larger in the sky than it
does today.
Forming the moon
Putting it all together:
The devil is in the details
To model the accumulation of the
moon from the impact-ejected debris,
SwRI researchers track the interactions
between particles as they orbit the Earth.
This is typically done by using an N-body
integration method, which explicitly
While the models of lunar accumulation easily account for why the Earth has
only one moon, they also suggest that the
accretion process is very inefficient, with
always less than half of the initially orbiting debris incorporated into the final
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moon. This, in turn, means that a more
massive initial debris cloud - one
containing at least two times the lunar
mass - must have been produced by the
impact to yield a lunar-sized moon. For
the past two years, SwRI staff have collaborated with Dr. Alastair Cameron, a
professor at Harvard University in
Cambridge, Massachusetts, to identify
which sizes and velocities of impactors, as
well as which impact angles, are capable
of producing sufficiently massive debris
disks to form the moon.
One class of impacts that characteristically places sufficient amounts of material into orbit involves bodies with three
times the mass of Mars and more than
twice the current system angular momentum. These impacts yield an Earth with a
moon of the correct size, but leave the system spinning too rapidly. From the basic
laws of physicS, it is known that the angular momentum of the Earth-moon system
has been very nearly conserved over the
age of the solar system, with a small
amount (less than 10 percent) lost to interaction with the sun. Thus, for these
extremely high angular momentum
impacts, one must invoke some mechanism to significantly slow the Earth' s spin
after the moon-forming event, such as perhaps a second massive impact.
Another class of possible impacts that
could produce an appropriately sized
moon yields the correct total angular
momentum, but results in an Earth that is
only 60 percent of its current mass. This
scenario is also problematic: If the Earth
continued to accumulate solar-orbiting
material in large amounts after the moon
Moon-forming Impact Simulation
could affect the ejecta yield predicted by
the SPH simulations that, to date, have
assumed Earth was not rotating prior to
the impact event.
These results suggest that new
regions of parameter space need to be
modeled using impact and accretion simulations to develop a consistent, plausible
model for the origin of the Earth-moon
system. Such research can then be applied
to models of the formation of the PlutoCharon system - also believed to be the
result of an impact event - as well as to
the formation of planets and moons in
solar systems around other stars.
Conclusions
Courtesy Dr. Alastair Cameron. Harvard University
A time sequence computer simulation (beginning top left) shows a potential moon-forming
impact modeled using the smoothed-particle hydrodynamics method. The mantles of the Earth
and impactor are represented by red particles that change to orange when heated, while the
iron cores are shown with blue particles that change to green with increasing temperature. The
initial impact imparts a counterclockwise spin to the Earth, and part of the impacting body
temporarily re-coalesces before colliding with the Earth a second time.
After the second hit, material primarily from the impactor's mantle is sheared into a disk of
debris; the total amount of iron left in orbit is consistent with the moon's small core. The total
time simulated by this run is about a day. Simulations such as this one demonstrated that a
Mars-sized body colliding with the Earth with something close to the current Earth-moon system
angular momentum could leave roughly a lunar mass worth of material in orbit.
was formed, it would have been difficult
to prevent the moon from becoming contaminated with iron-rich material
imported in such collisions as well.
Researchers have thus yet to identify a
set of impact conditions that yields the
Earth-moon system in the most widely
accepted paradigm for lunar origin.
Fortunately for the impact theory,
there are still many avenues to explore.
SwRl researchers are using an algorithm
developed by Levison to conduct the first
highly accurate simulations of the final
stages of terrestrial planet formation that
will explicitly track the dynamics of the
largest impact events. To date, results from
this work suggest that Earth-like planets
could experience several large impact
events and that the final masses and angular momentum of the Earth-moon system
may be the combined result of more than
one impact. Simulations have also shown
that Earth probably had a significant spin
prior to the moon-forming event, and this
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As we detect other planetary systems
that are quite different from our own, the
question that drew many astronomers and
planetary scientists into the field even as
children arises: Are there other Earths? By
learning more about the moon, we
become increasingly aware of its interactions with our planet. In particular, we
now know that the presence of our large
moon acts to stabilize the variation of the
Earth's rotational axis, a fact that was first
discovered in 1974 by SwRl Institute
Scientist Dr. William Ward, who was then
at the Harvard Center for Astrophysics.
Were it not for the moon, the influence of
the giant planets in our system would
cause Earth's obliquity - the angle
between the Earth's equator and the plane
of its orbit, whose current value is 23.5
degrees - to vary wildly with values as
extreme as 0 to 80 degrees. Such variation
would probably cause extreme climatic
changes that would render the planet
uninhabitable. Thus having a large moon
may be one of the key characteristics necessary for a habitable Earth-like planet making it all the more important to
resolve questions about the origin of our
Earth and moon. •:.
* Dr. William Hartmann and Dr. Don Davis
(both of the Planetary Science Institute), and
Dr. Alastair Cameron (Harvard University)
and Dr. William Ward (currently at SwRI,
but then at the Jet Propulsion Laboratory),
first proposed the giant impact scenario in
1976 and 1977.
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